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Math Help - Can anyone find any sort of order to this?

  1. #1
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    Can anyone find any sort of order to this?

    does anyone see any type of pattern in this? or is it totally random?


    40
    65
    110
    185
    310
    520
    870
    1450
    2420
    4040
    6750
    11270
    18820
    31430
    52490
    87660
    146395
    244480
    408280
    681825
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  2. #2
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    Quote Originally Posted by tek0011 View Post
    does anyone see any type of pattern in this? or is it totally random?


    40
    65
    110
    185
    310
    520
    870
    1450
    2420
    4040
    6750
    11270
    18820
    31430
    52490
    87660
    146395
    244480
    408280
    681825
    Where has the data come from?
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  3. #3
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    Quote Originally Posted by tek0011 View Post
    does anyone see any type of pattern in this? Or is it totally random?


    40
    65
    110
    185
    310
    520
    870
    1450
    2420
    4040
    6750
    11270
    18820
    31430
    52490
    87660
    146395
    244480
    408280
    681825
    Code:
     
    k          f(k)           error 
    0,        40.0,     40,  0.0
    1,        66.8,     65,  1.8
    2,       111.6,    110,  1.6
    3,       186.3,    185,  1.3
    4,       311.1,    310,  1.1
    5,       519.6,    520, -0.4
    6,       867.7,    870, -2.3
    7,      1449.0,   1450, -1.0
    8,      2419.9,   2420, -0.1
    9,      4041.2,   4040,  1.2
    10,     6748.8,   6750, -1.2
    11,    11270.4,  11270,  0.4
    12,    18821.6,  18820,  1.6
    13,    31432.2,  31430,  2.2
    14,    52491.7,  52490,  1.7
    15,    87661.1,  87660,  1.1
    16,   146394.1, 146395, -0.9
    17,   244478.1, 244480, -1.9
    18,   408278.4, 408280, -1.6
    19,   681825.0, 681825,  0.0
    20,  1138647.7
    21,  1901541.7
    22,  3175574.7
    23,  5303209.7
    24,  8856360.2
    25, 14790121.5
    26, 24699502.8
     f(k) = 10^{\left(0.222716k + 1.60206 \right)}

    .
    Not entirely random. If the function were to round to the nearest 5 value, then it looks as if your entire set could be matched.

    From where did those numbers originate?

    .
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  4. #4
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    Arrow

    Here is the full table. These numbers are for a game. The 1-20 is the level of the building. So for each of these sets does it look like it is rounding to the nearest 5? But I dont understand, because take the first set for example.

    1-2 Increase of 25
    2-3 Increase of 45
    3-4 Increase of 75
    and so on.

    I am trying to figure out if there is a formula or sequence they are following.
    Sorry, not very good at math at all, so layman's terms would be helpful.

    In essence what I want to do is copy their formula, but change the numbers slightly to fit our game. So I am wondering if there is some sort of sequence to it. Basically could I break those numbers down to give me a starting number. And then change that starting number, so the final number is different?
    For example (and this is completely incorrect, but the best way I can describe it)

    If to get to 40 they start with 5 , so 40/2 = 20, 20/2 = 10, 10/2 = 5
    then to get to 65 they start with 65/2 = 32.5, 32.5/2 = 16.25, 16.25/2 = 8.125
    ect. Is there a starting number they are using that we could then create a sequence of formula to come up with the increasing numbers.
    Does this make any sense at all?


    1 2 3 4
    1 40 100 50 60


    2 65 165 85 100


    3 110 280 140 165


    4 185 465 235 280


    5 310 780 390 465


    6 520 1300 650 780


    7 870 2170 1085 1300


    8 1450 3625 1810 2175


    9 2420 6050 3025 3630


    10 4040 10105 5050 6060


    11 6750 16870 8435 10125


    12 11270 28175 14090 16905


    13 18820 47055 23525 28230


    14 31430 78580 39290 47150


    15 52490 131230 65615 78740


    16 87660 219155 109575 131490


    17 146395 365985 182995 219590


    18 244480 611195 305600 366715


    19 408280 1020695 510350 612420


    20 681825 1704565 852280 1022740



    Sum 1699410 4248545 2124275 2549120
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  5. #5
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    Quote Originally Posted by tek0011 View Post
    Here is the full table.
    These numbers are for a game.
    The 1-20 is the level of the building.
    ...
    I am trying to figure out if there is a formula or sequence they are following.

    In essence what I want to do is copy their formula, but change the numbers slightly to fit our game. So I am wondering if there is some sort of sequence to it. Basically could I break those numbers down to give me a starting number. And then change that starting number, so the final number is different?

    If to get to 40 they start with 5 , so 40/2 = 20, 20/2 = 10, 10/2 = 5
    then to get to 65 they start with 65/2 = 32.5, 32.5/2 = 16.25, 16.25/2 = 8.125

    Is there a starting number they are using that we could then create a sequence of formula to come up with the increasing numbers.

    Does this make any sense at all?

    1 2 3 4
    1 40 100 50 60
    2 65 165 85 100
    3 110 280 140 165
    4 185 465 235 280
    5 310 780 390 465
    6 520 1300 650 780
    7 870 2170 1085 1300
    8 1450 3625 1810 2175
    9 2420 6050 3025 3630
    10 4040 10105 5050 6060
    11 6750 16870 8435 10125
    12 11270 28175 14090 16905
    13 18820 47055 23525 28230
    14 31430 78580 39290 47150
    15 52490 131230 65615 78740
    16 87660 219155 109575 131490
    17 146395 365985 182995 219590
    18 244480 611195 305600 366715
    19 408280 1020695 510350 612420
    20 681825 1704565 852280 1022740
    Sum 1699410 4248545 2124275 2549120
    Does this make any sense at all?
    NO. Some. Maybe. A little. Partially.

    A few new questions:
    What are columns 3, 4, & 5 supposed to represent?
    You did not have the sequence numbers (levels 1-20) in your original post when you listed all of the numeric values in column 2.
    Column 3 is greater than column 2; column 4 is less than column 3; and column 5 is greater than column 4.
    Does the summation (at the bottom) have any particular value?

    Do you want your numeric values to be mapped proportionately scaled?

    Using the funtion f(k) posted above:
    EXAMPLE 1
    to get the number for your Level 12:
    Since I started at zero, you started at 1.
    Your LEVEL 12 is equal to my sequence number 11

     11 \cdot 0.222716 = 2.449876

     2.449876 \, + \, 1.60206 \, = \, 4.051936

     10^{4.051936} = 11270.36

    Rounding 11270.3 to the nearest 5 --> 11270


    EXAMPLE 2
    Your LEVEL 17 is equal to my sequence number 16

     16 \cdot 0.222716 = 3.56346

     3.56346 \, + \, 1.60206 \, = \, 5.16552

     10^{5.16552} = 146393

    Rounding 146393 to the nearest 5 --> 146395

    ~~~
    It helps to understand the problem concept if all of the pertinent data is available initially.

    Could you elaborate on the additional data you put in your last post?

    .
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  6. #6
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    lol. Well. Columns 1-4 are a specific type of resource cost. So they dont have to be proportionally scaled.

    here is the spreadsheet in its entirety.



    Each column represents a cost of "imaginary resources". As they are probably not related to each other, Im assuming the levels themselves must be somehow proportionately scaled. Does your caculation seem to work for the other columns as well? Again, I am terrible at math. But can use your calculations to come up with a excel formula.
    What am I trying to do? Trying to figure out the formula of how they came up with the numbers in each column. Then once I figure out the formula, I can continue to divide the numbers to give me a start number. After I have a start number I can change that number by just a little bit to have the final number differ from what they have, but follow their same formula. This is really hard to explain, but i appreciate your patience and help trying to figure this out for me.
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  7. #7
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    to give a little better idea.

    say the numbers in column 1 were as follows:

    5
    10
    20
    40
    80
    etc

    it would be very easy for me to break it down and just change it to

    4
    8
    16
    32
    64
    etc

    but since i cant figure out if their formula is somehow sequenced or scaled, i cant create my own numbers. so hence why i am wondering if it it just randomly created.

    i suppose I could also use the total sum and proportionately break it down through 20 levels. I myself and now confused. HAHA
    Last edited by tek0011; September 24th 2009 at 11:54 AM. Reason: adding more
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  8. #8
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    Quote Originally Posted by tek0011 View Post
    lol. Well. Columns 1-4 are a specific type of resource cost. So they dont have to be proportionally scaled.

    here is the spreadsheet in its entirety.



    Each column represents a cost of "imaginary resources". As they are probably not related to each other, Im assuming the levels themselves must be somehow proportionately scaled. Does your caculation seem to work for the other columns as well? Again, I am terrible at math. But can use your calculations to come up with a excel formula.
    What am I trying to do? Trying to figure out the formula of how they came up with the numbers in each column. Then once I figure out the formula, I can continue to divide the numbers to give me a start number. After I have a start number I can change that number by just a little bit to have the final number differ from what they have, but follow their same formula. This is really hard to explain, but i appreciate your patience and help trying to figure this out for me.
    This is a computed table:

    ,40,100,50,60,
    ,1.602059991,2,1.698970004,1.77815125,<-Log(of 1st Value)
    ,0.2227165,0.2227165,0.2227165,0.2227165,<-log increment
    A, B, C, D, E
    1,40,100,50,60
    2,65,165,85,100
    3,110,280,140,165
    4,185,465,235,280
    5,310,780,390,465
    6,520,1300,650,780
    7,870,2170,1085,1300
    8,1450,3625,1810,2175
    9,2420,6050,3025,3630
    10,4040,10105,5050,6060
    11,6750,16870,8435,10125
    12,11270,28175,14090,16905
    13,18820,47055,23525,28230
    14,31430,78580,39290,47150
    15,52490,131230,65615,78740
    16,87660,219155,109575,131490
    17,146395,365985,182995,219590
    18,244480,611195,305600,366720
    19,408280,1020695,510350,612420
    20,681825,1704565,852280,1022740

    a is the value in column A from 1 to 20
    b is the value in column B matched with the value in column A.

    b = 10^{ 0.2227165 (a-1) + 1.602059991}
    b = INT[ b/5 + 0.5] \cdot 5
    'INT' is the integer function or floor function.

    ---
    The following are the formulas for an excel spread sheet.
    Code:
     
    ROW>A,    B,                                        C,                                     D,                                       E
    COL
    01] 0,   40,                                      100,                                     50,                                      60
    02] 0
    03] 0,   =LOG(B1),                                =LOG(C1),                                =LOG(D1),                                =LOG(E1),   <-Log(of 1st Value)
    04] 0
    05] 0,   0.2227165,                               0.2227165,                               0.2227165,                               0.2227165,   <-log increment
    06] 0
    07] 1,   =INT((10^(($A7-1)*B$5+B$3))/5+0.5)*5,    =INT((10^(($A7-1)*C$5+C$3))/5+0.5)*5,    =INT((10^(($A7-1)*D$5+D$3))/5+0.5)*5,    =INT((10^(($A7-1)*E$5+E$3))/5+0.5)*5
    08] 2,   =INT((10^(($A8-1)*B$5+B$3))/5+0.5)*5,    =INT((10^(($A8-1)*C$5+C$3))/5+0.5)*5,    =INT((10^(($A8-1)*D$5+D$3))/5+0.5)*5,    =INT((10^(($A8-1)*E$5+E$3))/5+0.5)*5   
    09] 3,   =INT((10^(($A9-1)*B$5+B$3))/5+0.5)*5,    =INT((10^(($A9-1)*C$5+C$3))/5+0.5)*5,    =INT((10^(($A9-1)*D$5+D$3))/5+0.5)*5,    =INT((10^(($A9-1)*E$5+E$3))/5+0.5)*5   
    10] 4,   =INT((10^(($A10-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A10-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A10-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A10-1)*E$5+E$3))/5+0.5)*5   
    11] 5,   =INT((10^(($A11-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A11-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A11-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A11-1)*E$5+E$3))/5+0.5)*5   
    12] 6,   =INT((10^(($A12-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A12-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A12-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A12-1)*E$5+E$3))/5+0.5)*5   
    13] 7,   =INT((10^(($A13-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A13-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A13-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A13-1)*E$5+E$3))/5+0.5)*5   
    14] 8,   =INT((10^(($A14-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A14-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A14-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A14-1)*E$5+E$3))/5+0.5)*5   
    15] 9,   =INT((10^(($A15-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A15-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A15-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A15-1)*E$5+E$3))/5+0.5)*5   
    16] 10,  =INT((10^(($A16-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A16-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A16-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A16-1)*E$5+E$3))/5+0.5)*5   
    17] 11,  =INT((10^(($A17-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A17-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A17-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A17-1)*E$5+E$3))/5+0.5)*5
    18] 12,  =INT((10^(($A18-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A18-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A18-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A18-1)*E$5+E$3))/5+0.5)*5
    19] 13,  =INT((10^(($A19-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A19-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A19-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A19-1)*E$5+E$3))/5+0.5)*5
    20] 14,  =INT((10^(($A20-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A20-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A20-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A20-1)*E$5+E$3))/5+0.5)*5
    21] 15,  =INT((10^(($A21-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A21-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A21-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A21-1)*E$5+E$3))/5+0.5)*5
    22] 16,  =INT((10^(($A22-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A22-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A22-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A22-1)*E$5+E$3))/5+0.5)*5
    23] 17,  =INT((10^(($A23-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A23-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A23-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A23-1)*E$5+E$3))/5+0.5)*5
    24] 18,  =INT((10^(($A24-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A24-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A24-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A24-1)*E$5+E$3))/5+0.5)*5
    25] 19,  =INT((10^(($A25-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A25-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A25-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A25-1)*E$5+E$3))/5+0.5)*5
    26] 20,  =INT((10^(($A26-1)*B$5+B$3))/5+0.5)*5,   =INT((10^(($A26-1)*C$5+C$3))/5+0.5)*5,   =INT((10^(($A26-1)*D$5+D$3))/5+0.5)*5,   =INT((10^(($A26-1)*E$5+E$3))/5+0.5)*5
    DecimalValue = 10^[(LEVEL - 1)*0.2227165 + log(FirstLevelNumber)]
    PointValue= INT(DecimalValue/5+0.5)*5
    The log values are common logs, not the natural logs.

    If you carefully enter the equation 1 time, you can replicate to all of the other cells.

    Hope that helps.
    If you have any questions or need additional information...

    .
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  9. #9
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    lol. that math is so far beyond anything i know. im lucky sometimes if i can remember multiplication tables. but if i look at things long enough ill figure them out. Ill have a question or two tomorrow. But the fact you already wrote the excel formulas? wow. thank you. Ill give them a try tomorrow.
    amazed at how people like you understand math so well.
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  10. #10
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    I'm very interested! I would love to find out more inforamtion related to this topic. Thanks in advance.
    me too, I need more detailed info
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